Question

simplify 32^1/5 +(-7)0 +(64)1/2

Answer 1

$( {2}^{5}) \frac{1}{5} + 1 + ({8}^{2} ) \frac{1}{2}$
2+1+8
=11

Answer 2

Given:   $(32)^\frac{1}{5} +(-7)^0+ (64)^\frac{1}{2}$

To Find : Evaluate

Solution:

$(32)^\frac{1}{5} +(-7)^0+ (81)^\frac{1}{2}$

$& {{\text{a}}^{n}}\times {{a}^{-n}}=1\text{ or }{{\text{a}}^{n}}=\frac{1}{{{a}^{n}}} \\ & {{a}^{m}}\times {{a}^{n}}={{a}^{m+n}} \\ & \frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}} \\ & {{\left( {{a}^{m}} \right)}^{n}}={{\left( {{a}^{n}} \right)}^{m}}={{a}^{mn}} \\ & {{a}^{m}}\times {{b}^{m}}={{\left( ab \right)}^{m}} \\ & \frac{{{a}^{n}}}{{{b}^{n}}}={{\left( \frac{a}{b} \right)}^{n}} \\ & {{a}^{0}}=1$

32 = 2⁵

64= 8²

$=(2^5)^\frac{1}{5} +(-7)^0+ (8^2)^\frac{1}{2}$

$=(2^1) +(-7)^0+ (8^1)$

= 2 + 1 + 8

= 11

$(32)^\frac{1}{5} +(-7)^0+ (64)^\frac{1}{2}=11$

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