Question

Use the Power Rule of Exponents to simplify (10^3)^6.(1 point)

Answer 1

If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses

(7^10)^5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline

(7⋅7⋅7⋅7⋅7)^10
left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline

(7^18)^3
left parenthesis 7 superscript 18 baseline right parenthesis cubed

(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)

Answer 2

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

Answer 3

Apply the Property of Negative Integer Exponents to solve 7^−3. The answer should not contain any exponent expression or decimals.(1 point)
7^−3=

Answer 4

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14 with positive exponents only.(1 point)
3^−17/8^−14=

Answer 5

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14 with positive exponents only.(1 point)
3^−17/8^−14=

Answer 6

Apply the Properties of Integer Exponents to generate equivalent expressions to (7^−3)^7 ⋅ 7^20/6^−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)
(7^−3)^7 ⋅ 7^20/6^−2=

Answer 7

Simplify the expression (4x^3)^2 using the properties of integer exponents.(1 point)
Responses

4x6
4 x superscript 6 baseline

16x6
16 x superscript 6 baseline

8x6
8 x superscript 6 baseline

16x5

Answer 8

Apply the properties of integer exponents to generate an equivalent algebraic expression to (4x4y−4)3(x7y3)2.(1 point)
Responses

x2y1864
Start Fraction x squared y superscript 18 baseline over 64 End Fraction

64x2y18
Start Fraction 64 over x squared y superscript 18 baseline End Fraction

64x20
Start Fraction 64 over x superscript 20 baseline End Fraction

4x2y18

Answer 9

choose a answer choice

Answer 10

Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7. Show your work and explain how you used the product rule of integer exponents.

Answer 11

The Power Rule of Exponents states that when you have a power of a power, you multiply the exponents.

Using this rule, we can simplify (10^3)^6 as follows:

(10^3)^6 = 10^(3*6) = 10^18

So, (10^3)^6 simplifies to 10^18.

Answer 12

The correct expanded equivalent expression of 7^15 using the Power Rule of Exponents would be:

(7^10)^5

Answer 13

Using the Power Rule of Exponents, we can simplify (19^4)^9 as follows:

(19^4)^9 = 19^(4*9) = 19^36

So, the simplified equivalent expression for (19^4)^9 is 19^36.

Answer 14

The Property of Negative Integer Exponents states that for any non-zero number a, a^(-n) is equal to 1/a^n.

Using this property, we can solve 7^(-3) as follows:

7^(-3) = 1/7^3 = 1/343

So, 7^(-3) is equal to 1/343.

Answer 15

The Property of Negative Integer Exponents states that for any non-zero number a, a^(-n) is equal to 1/a^n.

Applying this property to the expression 3^(-17)/8^(-14), we can convert the negative exponents to positive exponents:

3^(-17)/8^(-14) = (1/3^17)/(1/8^14)

Using the property of division, we can rewrite this expression as:

= (1 * 8^14)/(3^17 * 1)

= 8^14/3^17

So, the expression equivalent to 3^(-17)/8^(-14) with positive exponents only is 8^14/3^17.

Answer 16

To apply the Property of Negative Integer Exponents, we can convert the negative exponents to positive exponents by taking the reciprocal of the base.

For the expression 3^(-17)/8^(-14), we can rewrite it as:

1 / (3^17) * 1 / (8^14)

Taking the reciprocals of the bases, we get:

(1 / 3^17) * (1 / 8^14)

Now, we can simplify further by combining the terms with the same base:

1 / (3^17 * 8^14)

So, the expression equivalent to 3^(-17)/8^(-14) with positive exponents only is 1 / (3^17 * 8^14).

Answer 17

To simplify the expression using the properties of integer exponents, we'll start by applying the power of a power rule to (7^(-3))^7:

(7^(-3))^7 = 7^((-3) * 7) = 7^(-21)

Next, we can simplify the entire expression:

(7^(-3))^7 ⋅ 7^20/6^(-2) = 7^(-21) ⋅ 7^20/6^(-2)

Using the product of powers rule, we can combine the terms with the same base:

= 7^(-21 + 20) / 6^(-2)

Simplifying the exponent:

= 7^(-1) / 6^(-2)

Applying the power of a power rule to the numerator and denominator:

= 1/7^1 * 6^2

Simplifying further:

= 1/7 * 36

So, the expression (7^(-3))^7 ⋅ 7^20/6^(-2) simplifies to 1/7 * 36, which is equal to 36/7 as an improper fraction.

Answer 18

To simplify the expression (4x^3)^2 using the properties of integer exponents, we can apply the power of a power rule.

(4x^3)^2 = 4^2 * (x^3)^2 = 16 * x^(3*2)

Simplifying further, we get:

= 16 * x^6

So, the simplified expression is 16x^6.

Answer 19

To generate an equivalent algebraic expression to (4x^4y^-4)^3(x^7y^3)^2 using the properties of integer exponents, we can apply the product of powers rule and the power of a power rule.

Starting with (4x^4y^-4)^3, we have:

(4x^4y^-4)^3 = 4^3 * x^(4*3) * y^(-4*3) = 64 * x^12 * y^-12 = 64x^12 / y^12

Next, we multiply this by (x^7y^3)^2:

64x^12 / y^12 * (x^7y^3)^2 = 64x^12 / y^12 * x^(7*2) * y^(3*2) = 64x^12 / y^12 * x^14 * y^6 = 64x^(12+14) * y^(-12+6) = 64x^26 * y^-6

So, the equivalent algebraic expression is 64x^26 * y^-6.

Answer 20

I apologize for not providing answer choices in my response. Based on the simplification process I explained, the equivalent algebraic expression to (4x^4y^-4)^3(x^7y^3)^2 is:

64x^26 * y^-6

Answer 21

To find the numerical equivalent of 12^(-5)⋅12^7, we can apply the product rule of integer exponents, which states that when multiplying two numbers with the same base, we add their exponents.

Using this rule, we can simplify the expression as follows:

12^(-5)⋅12^7 = 12^(-5+7) = 12^2

So, the numerical equivalent is 12^2.

Simplifying further:

12^2 = 12 * 12 = 144

Therefore, the numerical equivalent of 12^(-5)⋅12^7 is 144.