Solve the expression 15⋅8^0/5+4(7^0−6) .(1 point)

Answer 1

The expression can be simplified step by step as follows:

First, let's simplify the exponents:

8^0 = 1 (Any number raised to the power of 0 equals 1)
7^0 = 1 (Same as above)

Now, we can proceed with the expression:

15⋅8^0/5+4(7^0−6)

We substitute the values for the exponents:

15⋅1/5+4(1−6)

Next, we simplify within the parentheses:

15⋅1/5+4(-5)

Multiplication and addition/subtraction are done from left to right:

3+4(-5)

Now we perform the multiplication:

3+(-20)

Finally, we add the numbers together:

3 - 20 = -17

So the final result is -17.

Answer 2

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

Answer 3

The Power Rule of Exponents states that when you have an exponent raised to another exponent, you multiply the exponents.

In this case, we have (10^3)^6.

To simplify, we multiply the exponents:

10^(3*6) = 10^18

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

Answer 4

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⋅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

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

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

Answer 5

The correct expanded equivalent expression using the Power Rule of Exponents for 7^15 would be (7⋅7⋅7⋅7⋅7)^10.
This is because 7^15 means 7 raised to the power of 15, which can be written as (7⋅7⋅7⋅7⋅7)^10, where the base 7 is multiplied by itself 10 times.

Answer 6

Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9 .(1 point)

Answer 7

To simplify the expression (19^4)^9 using the Power Rule of Exponents, we need to multiply the exponents.

(19^4)^9 can be expanded as:
19^(4*9)
19^36

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

Answer 8

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

Answer 9

The Property of Negative Integer Exponents states that any non-zero number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent.

Applying this property to 7^(-3), we can rewrite it as:

1 / 7^3

Now, let's calculate 7^3:

7^3 = 7 * 7 * 7 = 343

Therefore, 7^(-3) simplifies to 1 / 343.

Answer 10

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

Answer 11

To generate an expression equivalent to 3^(-17)/8^(-14) with positive exponents only, we can apply the Property of Negative Integer Exponents as follows:

Recall that any non-zero number raised to a negative exponent can be written as the reciprocal of the number raised to the positive exponent.

So, we can rewrite the given expression as:

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

Next, we can simplify this expression by applying the rule for dividing fractions:

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

Now, we can further simplify this expression by multiplying the numerators and multiplying the denominators:

(8^14) / (3^17)

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