Use the Product Rule of Exponents to simplify 5^10 x 5^5

Question

5^50
25^15
25^50
5^15

Find the numerical equivalent of 9^9x9^−6%0D%0A9%0D%0A9%0D%0A⋅%0D%0A9%0D%0A−%0D%0A6%0D%0A . Your answer should be written without exponents.

3. What is the missing exponent in the following equation? h^450/h^?=h^215

4. simplify 12^87 divide symbol 12^25

5. What is the missing number in this simplified exponential expression: 7^? divide symbol 7^5 = 7^12?

6. What is the value of 6.9−2^0%0D%0A6.9%0D%0A−%0D%0A2%0D%0A0%0D%0A?(1 point)%0D%0AResponses%0D%0A%0D%0A7.9%0D%0A7.9%0D%0A%0D%0A5.9%0D%0A5.9%0D%0A%0D%0A6.9%0D%0A6.9%0D%0A%0D%0A4.9

7. Apply the Zero Power Rule to create an equivalent expression to 9 x (-33)^0 + 3/2 (8-27^0) = _ x _ + 3/2 (_-_)

8. Solve the expression 15x8^0/5 + 4(7^0-6)

9. Use the Power Rule of Exponents to simplify (10^3)^6

10. If the expression 715%0D%0A7%0D%0A15%0D%0A was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)%0D%0AResponses%0D%0A%0D%0A(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)%0D%0A(%0D%0A7%0D%0A⋅%0D%0A7%0D%0A⋅%0D%0A7%0D%0A)%0D%0A⋅%0D%0A(%0D%0A7%0D%0A⋅%0D%0A7%0D%0A⋅%0D%0A7%0D%0A)%0D%0A⋅%0D%0A(%0D%0A7%0D%0A⋅%0D%0A7%0D%0A⋅%0D%0A7%0D%0A)%0D%0A⋅%0D%0A(%0D%0A7%0D%0A⋅%0D%0A7%0D%0A⋅%0D%0A7%0D%0A)%0D%0A⋅%0D%0A(%0D%0A7%0D%0A⋅%0D%0A7%0D%0A⋅%0D%0A7%0D%0A)%0D%0Aleft parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis%0D%0A%0D%0A(710)5%0D%0A(%0D%0A7%0D%0A10%0D%0A)%0D%0A5%0D%0Aleft parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline%0D%0A%0D%0A(7⋅7⋅7⋅7⋅7)10%0D%0A(%0D%0A7%0D%0A⋅%0D%0A7%0D%0A⋅%0D%0A7%0D%0A⋅%0D%0A7%0D%0A⋅%0D%0A7%0D%0A)%0D%0A10%0D%0Aleft parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline%0D%0A%0D%0A(718)3

11. Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9

12. Apply the Property of Negative Integer Exponents to solve 7−3%0D%0A7%0D%0A−%0D%0A3%0D%0A. The answer should not contain any exponent expression or decimals.

13. Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14%0D%0A3%0D%0A−%0D%0A17%0D%0A8%0D%0A−%0D%0A14%0D%0A with positive exponents only.(1 point)

14. Apply the Properties of Integer Exponents to generate equivalent expressions to (7^−3)^7 x 7^20/6^−2%0D%0A(%0D%0A7%0D%0A−%0D%0A3%0D%0A)%0D%0A7%0D%0A %0D%0A⋅%0D%0A %0D%0A7%0D%0A20%0D%0A6%0D%0A−%0D%0A2%0D%0A with only positive exponents, then solve the expression. Provide the answer as an improper fraction.

Answer 1

Let's solve the questions one at a time.

1. Simplify \(5^{10} \times 5^{5}\)

Using the Product Rule of Exponents: \[ 5^{10} \times 5^{5} = 5^{10 + 5} = 5^{15} \]

Answer: \(5^{15}\)

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2. Find the numerical equivalent of \(9^{9} \times 9^{-6}\)

Using the Property of Exponents: \[ 9^{9} \times 9^{-6} = 9^{9 - 6} = 9^{3} \]

Calculating \(9^{3}\): \[ 9^{3} = 729 \]

Answer: \(729\)

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3. What is the missing exponent in the equation \(h^{450}/h^{?} = h^{215}\)?

Using the Quotient Rule of Exponents: \[ h^{450 - ?} = h^{215} \implies 450 - ? = 215 \implies ? = 450 - 215 = 235 \]

Answer: \(235\)

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4. Simplify \(12^{87}/12^{25}\)

Using the Quotient Rule of Exponents: \[ 12^{87} / 12^{25} = 12^{87 - 25} = 12^{62} \]

Answer: \(12^{62}\)

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5. What is the missing number in the expression \(7^{?} / 7^{5} = 7^{12}\)?

Using the Quotient Rule of Exponents: \[ 7^{? - 5} = 7^{12} \implies ? - 5 = 12 \implies ? = 12 + 5 = 17 \]

Answer: \(17\)

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6. Evaluate \(6.9^{-2}\)

The expression \(6.9^{-2} = \frac{1}{6.9^{2}}\):

Calculating \(6.9^{2} = 47.61\):

Thus, \[ 6.9^{-2} = \frac{1}{47.61} \]

Keeping the answer in decimal is less clear, let's re-evaluate:

If simply to get value:

• Using direct calculation \(6.9 = \frac{1}{(6.9)^2}\approx 0.02041649\)

When using in approximation close enough to: Converting more:

Answer: \(0.0204\) or expressed simply as the round-off \(0.0208\) or \(5.9\).

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7. Apply the Zero Power Rule.

Using the Zero Power Rule: \[ (-33)^{0} = 1 \text{ and } 27^{0} = 1 \] Thus, the expression simplifies to: \[ 9 + \frac{3}{2}(8 - 1) = 9 + \frac{3}{2}(7) \]

Answer: \(9 \times 1 + \frac{3}{2} \times 7\)

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8. Solve \(15x8^{0}/5 + 4(7^{0}-6)\)

\[ 8^{0} = 1, \quad 7^{0} = 1 \] So, we have: \[ \frac{15 \times 1}{5} + 4(1 - 6) = 3 + 4(-5) = 3 - 20 = -17 \]

Answer: \(-17\)

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9. Simplify \((10^{3})^{6}\)

Using the Power Rule of Exponents: \[ (10^{3})^{6} = 10^{3 \times 6} = 10^{18} \]

Answer: \(10^{18}\)

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10. Expand \(7^{15}\)

The expanded equivalent expression for \(7^{15}\): \[ (7 \cdot 7 \cdot 7 \cdots 7) \text{ (15 times)} \]

Answer: \(7^{15} = (7 \cdots 7) \text{ (15 terms)}\)

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11. Simplify \((19^{4})^{9}\)

Using the Power Rule: \[ (19^{4})^{9} = 19^{4 \cdot 9} = 19^{36} \]

Answer: \(19^{36}\)

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12. Simplify \(7^{-3}\)

Using the positive exponent property: \[ 7^{-3} = \frac{1}{7^{3}} \] \[ 7^{3} = 343 \]

Answer: \(\frac{1}{343}\)

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13. Convert \(3^{-17}/8^{-14}\) to positive exponents.

\[ 3^{-17}/8^{-14} = \frac{3^{-17}}{8^{-14}} = \frac{8^{14}}{3^{17}} \text{ (by taking negative out)} \]

Answer: \(\frac{8^{14}}{3^{17}}\)

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14. Solve \((7^{-3})^{7} \cdot 7^{20}/6^{-2}\)

Step 1: Convert to positive exponents: \[ (7^{-3})^{7} = 7^{-21}, \quad 6^{-2} = \frac{1}{6^{2}} \]

Thus, simplifying: \[ \frac{7^{-21} \cdot 7^{20}}{6^{-2}} = \frac{7^{-21+20}}{1/6^{2}} = \frac{7^{-1}}{1/6^{2}} = \frac{6^{2}}{7^{1}} = \frac{36}{7} \]

Final Implied Answer: \[ \frac{36}{7} \]

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Answer 2

for question 7 *Answer: \(9 \times 1 + \frac{3}{2} \times 7\ - ___)**
there must be another number at the end ill show you where with the blank ___

Answer 3

Thank you for pointing that out! Let's revisit question 7 to ensure we include all the necessary elements to fill in the blank.

The expression given was: \[ 9 \times (-33)^0 + \frac{3}{2} (8 - 27^0) = _ \times _ + \frac{3}{2} (_ - _) \]

Break it down:

1. Recall that \( (-33)^0 = 1 \) and \( 27^0 = 1 \).
2. Thus, the expression becomes: \[ 9 \times 1 + \frac{3}{2} (8 - 1) \]
3. Simplifying within the parentheses: \[ 8 - 1 = 7 \]
4. So, we have: \[ 9 + \frac{3}{2} \times 7 \]

Now translating it to the form \( _ \times _ + \frac{3}{2} ( _ - _) \):

• The first part, \( _ \times _ \) can be \( 9 \times 1 \).
• For the second part, \( 8 \) and \( 1 \) fits nicely into \( \frac{3}{2} ( _ - _) \).

Putting it all together, we get: \[ 9 \times 1 + \frac{3}{2} (8 - 1) = 9 \times 1 + \frac{3}{2} (8 - 1) \]

Thus, replacing the blank (__) in the form: \[ = 9 \times 1 + \frac{3}{2} (8 - 1) \]

Final Fill:

• The last part filled is \( (8 - 1) \).

So, providing the complete response: Answer: \(9 \times 1 + \frac{3}{2} (8 - 1)\).

Answer 4

WOW!!! incredible litterally 1 wrong! okay 10 is 7x7x7 7x7x7x7x7 that thing with no exponents its just 7x7x7x7x77x7x7x7x

Answer 5

I appreciate your patience and feedback! Let's address question 10 correctly.

The statement you provided suggests that you're looking for the expanded version of \(7^{15}\) without using exponents:

10. Expand \(7^{15}\):

The expanded equivalent expression for \(7^{15}\) would indeed be: \[ 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \]

This means writing out \(7\) multiplied by itself \(15\) times:

Answer: \(7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7\)

Thank you for your understanding, and I'm glad to assist further! If you have any more questions or need clarifications, just let me know!