Question

evaluate
2¼×8¼
please answer this ASAP!​

Answer 1

• Solution -

$\implies\sf2^{ \frac{1}{4}} \times 8^{\frac{1}{4} }$

$\implies\sf2^{ \frac{1}{4}} \times ({2}^{3}) ^{\frac{1}{4} }$

$\implies\sf2^{ \frac{1}{4}} \times {2}^{3 \times\frac{1}{4}}$

$\implies\sf2^{ \frac{1}{4}} \times {2}^{\frac{3}{4}}$

$\implies\sf2^{{ \frac{1}{4} + {\frac{3}{4}}}}$

$\implies\sf2^\frac{1 + 3}{4}$

$\implies\sf2^\frac{4}{4}$

$\implies\sf2^\frac{ \not4}{ \not4}$

$\implies\sf2^1$

$\implies\sf2$

 • Know MorE -

$\red{\bigstar}$   Laws of Indices -

1st Law (Product Law)

For example -

$:  \implies\sf{ {a}^{2} \times  {a}^{3} =  {a}^{2 + 3}   }$

$:  \implies\sf{ {a}^{5}   }$

2nd Law  (Quotient law)

For example -

$: \implies\sf{ \dfrac{a^{2} }{a^{3}} }$

$: \implies\sf{a^{2 - 3} }$

$: \implies\sf{a^{ - 1} }$

3rd Law (Power law)

For example -

$: \implies\sf{(a^2)^3}$

$: \implies\sf{(a^{2 \times 3})}$

$: \implies\sf{(a^{6})}$

Answer 2

there are 2 ways of doing this.

FIRST METHOD

2^1/4 × 8^1/4 can be written as

2^1/4 × (2³)^1/4 (since 2×2×2=8) = 2^1/4 × 2^3/4 (as (aⁿ)ᵇ = aᵇˣⁿ

as the bases are equal I can use the exponent law (aᵇ × aⁿ = aᵇ⁺ⁿ)

2^1/4+3/4 = 2^4/4 = 2¹

SECOND METHOD

if the powers are the same,

aⁿ × bⁿ = (a×b)ⁿ

2^1/4 × 8^1/4 = (2×8)^1/4 = 16^1/4

hope it helps

have a great day