Step-by-step explanation:
3²×(3³)² × 3^-8
(3³)² = 3⁶
remember that an exponent of an exponent means to multiply the 2 exponents.
3²×3⁶ = 3⁸
remember that when we multiply the same base number with exponents, we add these exponents.
and then 3⁸×3^‐8 = 3⁰ = 1
3²×(2×3)^-3 / (2^-3)
(2×3)^-3 = 2^-3 × 3^-3
remember that an exponent of a product means that that exponent has to be applied to every factor.
so, 2^-3 / 2^-3 = 1
that leaves us with 3²×3^-3
remember that we add the exponents in such a case.
2 + -3 = -1
so, we get 3^-1 = 1/3
remember that a negative exponent just means 1/...
2^-1 × (2×3)⁴ / (2×3)³
this is now easy.
(2×3)⁴ / (2×3)³ = (2×3)¹ = 2×3
and then
2^-1 × 2¹×3¹ = 2⁰×3¹ = 1×3 = 3
2⁵×3⁵×6^-5 = (2×3)⁵ × 6^-5 = 6⁵×6^-5 = 6⁰ = 1
2³×(2×3)^-1 / 2²
2³/2² = 2¹ = 2
2¹×(2×3)^-1 = 2¹×2^-1 × 3^-1 = 2⁰×3^-1 = 1×3^-1 = 3^-1 = 1/3
