Question

simplify 2^2/3*2^1/3

Answer 1

2^(2/3) × 2^(1/3)

=(2)^(2/3 +1/3)

=(2)^(3/3)

=(2)^(1)

=2

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Answer 2

Answer:

After simplication value of the given expression is 2.

Step-by-step explanation:

Given expression is ${2}^{ \frac{2}{3} } \times {2}^{ \frac{1}{3} }$

This is a problem of Power of indices.

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

Here applied formulas are,

${x}^{a} \times {x}^{b} = {x}^{a + b}$

${x}^{1} = x$

Some important formulas of power of indices,

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$