14 Simplify (2a)−4 × 3a2. log8 + log 4.

a) Step 1: Apply the exponent rule (xy)ⁿ = xⁿ yⁿ to the first term. (2a)⁻⁴ × 3a³ = (2⁻⁴ a⁻⁴) × 3a³ Step 2: Calculate 2⁻⁴ and combine the constant terms. (1)/(2⁴) a⁻⁴ × 3a³ = 1/16 a⁻⁴ × 3a³; Step 3: Multiply the terms with a using the rule x^m × xⁿ = x^(m+n). 3/16 a⁻⁴⁺³ = 3/16 a⁻¹ Step 4: Express a⁻¹ as 1/a. 3/16a The simplified expression is: 3/16a b) Step 1: Apply the logarithm property log x + log y = log (xy). log 8 + log 4 = log (8 × 4) Step 2: Perform the multiplication. log 32 The simplified expression is: log 32

14 Simplify (2a)−4 × 3a2. log8 + log 4.

a) Step 1: Apply the exponent rule (xy)ⁿ = xⁿ yⁿ to the first term. (2a)⁻⁴ × 3a³ = (2⁻⁴ a⁻⁴) × 3a³ Step 2: Calculate 2⁻⁴ and combine the constant terms. (1)/(2⁴) a⁻⁴ × 3a³ = 1/16 a⁻⁴ × 3a³; Step 3: Multiply the terms with a using the rule x^m × xⁿ = x^(m+n). 3/16 a⁻⁴⁺³ = 3/16 a⁻¹ Step 4: Express a⁻¹ as 1/a. 3/16a The simplified expression is: 3/16a b) Step 1: Apply the logarithm property log x + log y = log (xy). log 8 + log 4 = log (8 × 4) Step 2: Perform the multiplication. log 32 The simplified expression is: log 32

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14 Simplify (2a)-4 x 3a2. log8 + log 4.

September 23, 2026Mathematics

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Answers

2 parts

\frac{3}{16a}

\log 32

Step-by-step solution

6 steps

Part a· 4 steps

Apply the exponent rule $(xy)^n = x^n y^n$ to the first term.
$(2a)^{-4} \times 3a^3 = (2^{-4} a^{-4}) \times 3a^3$
Calculate $2^{-4}$ and combine the constant terms.
$\frac{1}{2^4} a^{-4} \times 3a^3 = \frac{1}{16} a^{-4} \times 3a^3$
Multiply the terms with $a$ using the rule $x^m \times x^n = x^{m+n}$ .
$\frac{3}{16} a^{-4+3} = \frac{3}{16} a^{-1}$
Express $a^{-1}$ as $\frac{1}{a}$ .
$\frac{3}{16a}$
The simplified expression is:
$\boxed{\frac{3}{16a}}$

Part b· 2 steps
$\log 32$

Apply the logarithm property $\log x + \log y = \log (xy)$ .
$\log 8 + \log 4 = \log (8 \times 4)$
Perform the multiplication.
$\log 32$
The simplified expression is:
$\boxed{\log 32}$

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14 Simplify (2a)-4 x 3a2. log8 + log 4.

Answers

Step-by-step solution

Part a· 4 steps

Apply the exponent rule (xy)n=xnyn(xy)^n = x^n y^n(xy)n=xnyn to the first term.

Calculate 2−42^{-4}2−4 and combine the constant terms.

Multiply the terms with aaa using the rule xm×xn=xm+nx^m \times x^n = x^{m+n}xm×xn=xm+n.

Express a−1a^{-1}a−1 as 1a\frac{1}{a}a1​.

Part b· 2 stepslog⁡32\log 32log32

Apply the logarithm property log⁡x+log⁡y=log⁡(xy)\log x + \log y = \log (xy)logx+logy=log(xy).

Perform the multiplication.

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More Mathematics Questions

Apply the exponent rule $(xy)^n = x^n y^n$ to the first term.

Calculate $2^{-4}$ and combine the constant terms.

Multiply the terms with $a$ using the rule $x^m \times x^n = x^{m+n}$ .

Express $a^{-1}$ as $\frac{1}{a}$ .

Part b· 2 steps
$\log 32$

Apply the logarithm property $\log x + \log y = \log (xy)$ .