Question

In which expression should the exponents be multiplied?

A.one fifth to the 2nd times one fifth to the 6th
B. 9 to the 3rd over 9 to the 4th
C. 73 ⋅ 78
D. (26)−5

Answer 1

the answer is D

Explanation:

Answer 2

D. (2^6)^-5

Explanation:

The exponent rules are ...

`a^ba^c=a^(b+c)\\\\(a^b)^c=a^(bc)`

Exponents are multiplied when an exponential expression is raised to a power.

A.

`\left((1)/(5)\right)^2\left((1)/(5)\right)^6=\left((1)/(5)\right)^(2+6)=\left((1)/(5)\right)^8 \quad\text{exponents added}`

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B.

`(9^3)/(9^4)=(9^3)(9^(-4))=9^(3-4)=9^(-1) \quad\text{exponents added}`

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C.

`(7^3)(7^(8))=7^(3+8)=7^(11) \quad\text{exponents added}`

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D.

`(2^6)^(-5)=2^(6(-5))=2^(-30) \quad\text{\bf{exponents multiplied}}`