Complete the Expression: (3×7)/(4×8) Raised to Power (b+1)

Insert the corresponding expression:

$\left(\frac{3\times7}{4\times8}\right)^{b+1}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:04 According to the laws of exponents, a fraction raised to a power (N)

00:08 equals the numerator and denominator raised to the same power (N)

00:13 We will apply this formula to our exercise

00:21 According to the laws of exponents when a product is raised to a power (N)

00:26 it is equal to each factor in the product separately raised to the same power (N)

00:33 We will apply this formula to our exercise

00:47 This is the solution

Step-by-Step Solution

To solve the expression $\left(\frac{3\times7}{4\times8}\right)^{b+1}$ , we follow these steps:

Step 1: Apply the power $(b+1)$ to the entire fraction, $\left(\frac{3 \times 7}{4 \times 8}\right)^{b+1}$ .
Step 2: Use the exponentiation rule $(\frac{a}{b})^n = \frac{a^n}{b^n}$ to apply the power to both numerator and denominator separately.
Step 3: Expand the numerator and the denominator: $(3 \times 7)^{b+1} = 3^{b+1} \times 7^{b+1}$ and $(4 \times 8)^{b+1} = 4^{b+1} \times 8^{b+1}$ .
Step 4: Combine these results into one fraction: $\frac{3^{b+1} \times 7^{b+1}}{4^{b+1} \times 8^{b+1}}$ .

Therefore, the simplified expression is $\frac{3^{b+1}\times7^{b+1}}{4^{b+1}\times8^{b+1}}$ .

Upon examining the choices, the correct option is choice 3: $\frac{3^{b+1}\times7^{b+1}}{4^{b+1}\times8^{b+1}}$ .