If $p$ is a positive integer, what is the value of... | Free GMAT Practice Question | GMAT Panda

👋 Hi! I'm GMAT Panda. Ask me anything about this question, or click a button below to get started!

If p is a positive integer, what is the value of ((- 5)^{p})^{- 2} + (5^{- p})^{2} ?

Explanation	Calculations	Help
$We simplify the first term by applying the power-of-a-power rule while keeping the expression in literal form.$	$((- 5)^{p})^{- 2} = (- 5)^{- 2 p} = (- 1)^{- 2 p} \times 5^{- 2 p} = 1 \times 5^{- 2 p} = 5^{- 2 p}$	Theory & Tactics Method Card CALC3-A Click to view full details
$We simplify the second term by applying the power-of-a-power rule to combine the exponents.$	$(5^{- p})^{2} = 5^{- 2 p}$	Theory & Tactics Method Card CALC3-A Click to view full details
$We add the two identical terms by grouping like terms.$	$5^{- 2 p} + 5^{- 2 p} = 2 \times 5^{- 2 p}$	Theory & Tactics Method Card CALC1-A Click to view full details

Scroll horizontally to view all columns

C

If p is a positive integer, what is the value of ((- 5)^{p})^{- 2} + (5^{- p})^{2} ?

Explanation	Calculations	Help
$We simplify the first term by applying the power-of-a-power rule while keeping the expression in literal form.$	$((- 5)^{p})^{- 2} = (- 5)^{- 2 p} = (- 1)^{- 2 p} \times 5^{- 2 p} = 1 \times 5^{- 2 p} = 5^{- 2 p}$	Theory & Tactics Method Card CALC3-A Click to view full details
$We simplify the second term by applying the power-of-a-power rule to combine the exponents.$	$(5^{- p})^{2} = 5^{- 2 p}$	Theory & Tactics Method Card CALC3-A Click to view full details
$We add the two identical terms by grouping like terms.$	$5^{- 2 p} + 5^{- 2 p} = 2 \times 5^{- 2 p}$	Theory & Tactics Method Card CALC1-A Click to view full details

Scroll horizontally to view all columns

C