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GMAT Quant — Algebra (Exponents)

If (5^{p})^{q} = 5^{7} and p and q are positive integers, what is the value of 5^{p} \times 5^{q} ?

Explanation	Calculations	Help
$We rewrite the left side using exponent rules and then set the exponents equal because the base is 5 on both sides.$	$(5^{p})^{q} = 5^{7} 5^{pq} = 5^{7} pq = 7$	Theory & Tactics Method Card EXP3 Click to view full details
$We list the positive integer pairs that multiply to 7.$	$p \times q = 7 (p, q) = (1, 7) or (7, 1)$
$We add the exponents to get the combined exponent and then evaluate the power of 5.$	$5^{p} \times 5^{q} = 5^{p + q} = 5^{1 + 7} or 5^{7 + 1} = 5^{8}$

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C

GMAT Quant — Algebra (Exponents)

If (5^{p})^{q} = 5^{7} and p and q are positive integers, what is the value of 5^{p} \times 5^{q} ?

Explanation	Calculations	Help
$We rewrite the left side using exponent rules and then set the exponents equal because the base is 5 on both sides.$	$(5^{p})^{q} = 5^{7} 5^{pq} = 5^{7} pq = 7$	Theory & Tactics Method Card EXP3 Click to view full details
$We list the positive integer pairs that multiply to 7.$	$p \times q = 7 (p, q) = (1, 7) or (7, 1)$
$We add the exponents to get the combined exponent and then evaluate the power of 5.$	$5^{p} \times 5^{q} = 5^{p + q} = 5^{1 + 7} or 5^{7 + 1} = 5^{8}$

Scroll horizontally to view all columns

C