Question

${x}^{x {}^{3 \div 2} } = {x}^{(3 \div 2)x}$
what is the value of x

Answer 1

Hello Friend

Here is your answer

${x}^{ {x}^{3 \div 2} } = {x}^{(3 \div 2)x} \\ \\ as \: same \: base \: so \: power \: is \: same \\ \\ {x}^{ \frac{3}{2} } = \frac{3}{2} x \\ \\ ( \sqrt{x} ) {}^{3} = \frac{3}{2} x \\ \\ \sqrt{x} \times \sqrt{x} \times \sqrt{x} = \frac{3}{2} x \\ \\ x \sqrt{x} = \frac{3}{2} x \\ \\ \sqrt{x} = \frac{3}{2} \\ \\ on \: squaring \: both \: sides \: we \: get \\ \\ ( \sqrt{x} ) {}^{2} = ( \frac{3}{2} ) {}^{2} \\ \\ x = \frac{9}{4}$

Hope it helps you

Answer 2

Answer is

${x}^{ {x}^{3 \div 2} } = {x}^{(3 \div 2)x} \\ \\ as \: same \: base \: so \: power \: is \: same \\ \\ {x}^{ \frac{3}{2} } = \frac{3}{2} x \\ \\ ( \sqrt{x} ) {}^{3} = \frac{3}{2} x \\ \\ x \sqrt{x} = \frac{3}{2} x \\ \\ \sqrt{x} = \frac{3}{2} \\ \\ ( \sqrt{x} ) {}^{2} = ( \frac{3}{2} ) {}^{2} \\ \\ x = \frac{9}{4}$

Hope it helps you

@ MSD