Find the value of n- if5-32 n -1-5-35-5-3 n -2 -A- n -4B- n -0C- n -1D- n -4

The correct option is D n= 4By the Laws of exponents , we know that a^m × a^n=a^m+n ⇒ (5/3)^2n+1× (5/3)^5=(5/3)^2n+1+5 ⇒ (5/3)^2n+6=(5/3)^n+2 Since the base ...

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Byju's Answer

Standard VII

Mathematics

Exponents with Like Bases

Find the valu...

Question

Find the value of n, if

$(\frac{5}{3})^{2 n + 1} \times (\frac{5}{3})^{5} = (\frac{5}{3})^{n + 2} .$

n = 4

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n = 1

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n = - 4

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n = 0

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Solution

The correct option is C $n = - 4$
By the Laws of exponents , we know that $a^{m} \times a^{n} = a^{m + n}$

$\Rightarrow (\frac{5}{3})^{2 n + 1} \times (\frac{5}{3})^{5} = (\frac{5}{3})^{2 n + 1 + 5}$

$\Rightarrow (\frac{5}{3})^{2 n + 6} = (\frac{5}{3})^{n + 2}$

Since the bases are same, we can equate the powers.

$\Rightarrow 2 n + 6 = n + 2 \Rightarrow 2 n - n = 2 - 6 \Rightarrow n = - 4$

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Similar questions

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Find the value of n, if (53)2n+1×(53)5=(53)n+2.

The correct option is C n=−4By the Laws of exponents , we know that am×an=am+n ⇒(53)2n+1×(53)5=(53)2n+1+5 ⇒(53)2n+6=(53)n+2 Since the bases are same, we can equate the powers. ⇒2n+6=n+2⇒2n−n=2−6⇒n=−4

Find the value of n, if

$(\frac{5}{3})^{2 n + 1} \times (\frac{5}{3})^{5} = (\frac{5}{3})^{n + 2} .$