May 2026

Find (x+1)^2 Question \[ (x-1)^3 = 8 \] Solution \[ 8 = 2^3 \] \[ (x-1)^3 = 2^3 \] \[ x – 1 = 2 \] \[ x = 3 \] \[ (x+1)^2 = (3+1)^2 \] \[ = 4^2 \] \[ = 16 \] Answer \[ \boxed{16} \] Next Question / Full Exercise

Simplify Step-wise Question \[ \left[\{625^{-1/2}\}^{-1/4}\right]^2 \] Solution \[ 625 = 5^4 \] \[ = \left[\{(5^4)^{-1/2}\}^{-1/4}\right]^2 \] \[ = \left[(5^{-2})^{-1/4}\right]^2 \] \[ = \left[5^{1/2}\right]^2 \] \[ = 5 \] Answer \[ \boxed{5} \] Next Question / Full Exercise

Find Value of Given Expression Question \[ \{5(8^{1/3}+27^{1/3})^3\}^{1/4} \] Solution \[ 8^{1/3} = 2,\quad 27^{1/3} = 3 \] \[ = \{5(2+3)^3\}^{1/4} \] \[ = \{5 \cdot 5^3\}^{1/4} \] \[ = \{5^4\}^{1/4} \] \[ = 5 \] Answer \[ \boxed{5} \] Next Question / Full Exercise

Find Value of ∛(125 × 27) Question \[ \sqrt[3]{125 \times 27} \] Solution \[ 125 = 5^3,\quad 27 = 3^3 \] \[ = \sqrt[3]{5^3 \times 3^3} \] \[ = \sqrt[3]{(15)^3} \] \[ = 15 \] Answer \[ \boxed{15} \] Next Question / Full Exercise

Convert to Rational Number Question \[ \left(\frac{1}{9}\right)^{-1/2} \times 64^{-1/3} \] Solution \[ \left(\frac{1}{9}\right)^{-1/2} = 9^{1/2} \] \[ = 3 \] \[ 64^{-1/3} = \frac{1}{64^{1/3}} \] \[ = \frac{1}{4} \] \[ = 3 \times \frac{1}{4} \] \[ = \frac{3}{4} \] Answer \[ \boxed{\frac{3}{4}} \] Next Question / Full Exercise

Find Value of ∛7 × ∛49 Question \[ \sqrt[3]{7} \times \sqrt[3]{49} \] Solution \[ = \sqrt[3]{7 \times 49} \] \[ 49 = 7^2 \] \[ = \sqrt[3]{7 \times 7^2} \] \[ = \sqrt[3]{7^3} \] \[ = 7 \] Answer \[ \boxed{7} \] Next Question / Full Exercise

Find x/y Question \[ 3^{x-1}=9,\quad 4^{y+2}=64 \] Solution \[ 9=3^2 \Rightarrow 3^{x-1}=3^2 \] \[ x-1=2 \Rightarrow x=3 \] \[ 64=4^3 \Rightarrow 4^{y+2}=4^3 \] \[ y+2=3 \Rightarrow y=1 \] \[ \frac{x}{y}=\frac{3}{1}=3 \] Answer \[ \boxed{3} \] Next Question / Full Exercise

Find x Question \[ 2^4 \times 4^2 = 16^x \] Solution \[ 4 = 2^2,\quad 16 = 2^4 \] \[ 2^4 \times (2^2)^2 = (2^4)^x \] \[ 2^4 \times 2^4 = 2^{4x} \] \[ 2^8 = 2^{4x} \] \[ 8 = 4x \] \[ x = 2 \] Answer \[ \boxed{2} \] Next Question /

Power Law of Exponents Statement \[ (a^m)^n = a^{mn} \] Condition \[ a \neq 0,\quad m,n \in \mathbb{R} \] Answer \[ \boxed{(a^m)^n = a^{mn}} \] Next Question / Full Exercise

Quotient Law of Exponents Statement \[ \frac{a^m}{a^n} = a^{m-n} \] Condition \[ a \neq 0,\quad m,n \in \mathbb{R} \] Answer \[ \boxed{\frac{a^m}{a^n} = a^{m-n}} \] Next Question / Full Exercise