Calculate the value 2-34-2-32-4-92 k -3A- 7B- 6C- 3D- 2

The correct option is C 3(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 ...

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Byju's Answer

Standard VII

Mathematics

Combination of n Different Things Taken One or More at a Time

Calculate the...

Question

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

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Solution

The correct option is A 3
$(\frac{2}{3})^{4} \times (\frac{2}{3})^{2} = (\frac{4}{9})^{(2 k - 3)}$
$(\frac{2}{3})^{4 + 2} = (\frac{2}{3})^{2 (2 k - 3)}$
$(\frac{2}{3})^{6} = (\frac{2}{3})^{2 (2 k - 3)}$
Comparing the powers of similar base, we get
6 = 2(2k - 3)
6 = 4k - 6
6 + 6 = 4k
12 = 4k
k = $\frac{12}{4}$ = 3

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Similar questions

Q. Calculate the value of

k

if,

(\frac{2}{3})^{4} \times (\frac{2}{3})^{2} = (\frac{4}{9})^{(2 k - 3)}

\frac{3 a + 7 b}{3 a - 7 b} = \frac{4}{3}

then find the value of the ratio

\frac{3 a^{2} - 7 b^{2}}{3 a^{2} + 7 b^{2}}

Q. If

\frac{3 a + 7 b}{3 a - 7 b} = \frac{4}{3}

then find the value of the ratio

\frac{3 a^{2} - 7 b^{2}}{3 a^{2} + 7 b^{2}}

Q. Question 10
The value of

2 \sqrt{3} + \sqrt{3}

is

A)

2 \sqrt{6}

B) 6
C)

3 \sqrt{3}

4 \sqrt{6}

If $x = \frac{2}{3 + \sqrt{7}}$ , then $(x - 3)^{2}$ =

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

The correct option is A 3(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 - 6 6 + 6 = 4k 12 = 4k k = 124= 3

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