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

Question

asked Oct 12, 2018 138k views

2 Answers

Aqwsez · Answer 1 · 2018-10-18T11:22:50+0000

Answer:

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.

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