Maths / Exponents and Power / Statement Sums Involving Exponent and Power

QUESTION

Find the values of n in the following: $\dpi{120} \fn_jvn \large (2/3)^{10}\times((3/2)^2)^5 = (2/3)^{2n-2}$

 OPTIONS A. 1 B. 0 C. 2 D. 3
Right Option : A

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{120} \fn_jvn \large (2/3)^{10}\times((3/2)^2)^5 = (2/3)^{2n-2}$

$\large =(2/3)^{10}\times(3/2)^1^0 = (2/3)^{2n-2}$

$\dpi{120} \large =(2/3)^{10}\times(2/3)^-^1^0 = (2/3)^{2n-2}$

$\dpi{120} \large =(2/3)^{0}= (2/3)^{2n-2}$

When bases are same powers are equated

0 = 2n - 2

2n = 2

n = 1

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