Calculate the value of k if- 2-34 - 2-32-4-92k-3

Given: nbsp;(2/3)^4 × (2/3)^2=(4/9)^(2k 3) (2/3)^4+2=(2/3)^2(2k 3) (2/3)^6=(2/3)^2(2k 3) Comparing the powers of similar base, we get 6 = 2(2k 3) 6 = 4k ...

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Standard X

Mathematics

Exponents

Calculate the...

Question

Calculate the value of $k$ if,
$(\frac{2}{3})^{4} \times (\frac{2}{3})^{2} = (\frac{4}{9})^{(2 k - 3)}$

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Solution

The correct option is A 3
Given: $(\frac{2}{3})^{4} \times (\frac{2}{3})^{2} = (\frac{4}{9})^{(2 k - 3)}$
$(\frac{2}{3})^{4 + 2} = (\frac{2}{3})^{2 (2 k - 3)}$
$(\frac{2}{3})^{6} = (\frac{2}{3})^{2 (2 k - 3)}$

Comparing the powers of similar base, we get
$6 = 2 (2 k - 3) 6 = 4 k - 6 6 + 6 = 4 k 12 = 4 k k = \frac{12}{4} = 3$

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Calculate the value of k if, (23)4×(23)2=(49)(2k−3)

The correct option is A 3Given: (23)4×(23)2=(49)(2k−3) (23)4+2=(23)2(2k−3) (23)6=(23)2(2k−3) Comparing the powers of similar base, we get 6=2(2k−3)6=4k−66+6=4k12=4kk=124=3

Calculate the value of $k$ if,
$(\frac{2}{3})^{4} \times (\frac{2}{3})^{2} = (\frac{4}{9})^{(2 k - 3)}$