Question

(a^3b/c^4)^5*(c^7/a^5b^2)^3

Answer 1

Ответ: c/b

Объяснение:

=a^15*b^5*c^21 /c^20*a^15*b^6 =c/b

Answer 2

To simplify the expression $(a^3b/c^4)^5 \cdot (c^7/a^5b^2)^3$, we'll follow the order of operations, which involves simplifying the terms within each set of parentheses and then performing the multiplication.

Let's simplify each term within the parentheses:

1. $(a^3b/c^4)^5$ can be simplified by applying the exponent to each term inside the parentheses: $(a^3b/c^4)^5 = a^{3 \cdot 5} \cdot b^5 / c^{4 \cdot 5} = a^{15} \cdot b^5 / c^{20}$.

2. $(c^7/a^5b^2)^3$ can be simplified similarly: $(c^7/a^5b^2)^3 = c^{7 \cdot 3} / (a^{5 \cdot 3} \cdot b^{2 \cdot 3}) = c^{21} / (a^{15} \cdot b^6)$.

Now, we'll multiply the simplified terms together:

$(a^{15} \cdot b^5 / c^{20}) \cdot (c^{21} / (a^{15} \cdot b^6))$.

When multiplying fractions, we can cancel out common terms from the numerator of one fraction with the denominator of the other fraction:

$(a^{15} \cdot b^5 \cdot c^{21}) / (c^{20} \cdot a^{15} \cdot b^6)$.

Now, simplify the common terms in the numerator and denominator:

$(a^{15} \cdot b^5 \cdot c^{21}) / (a^{15} \cdot b^6 \cdot c^{20})$.

Since the bases are the same (a, b, c), you can subtract the exponents in the denominator from the exponents in the numerator:

$a^{15-15} \cdot b^{5-6} \cdot c^{21-20} = a^0 \cdot b^{-1} \cdot c^1 = c / b$.

So, the simplified expression is $c/b$.