Write as a single power of 2:
a. 4^10
b. 8^x times 2^4
c. 16^2/3
d. 2^x times 4^y times 8^z times 16
e. 2√2
f. 4/3√2
g. 4^1/3 times 8^1/5

Let's rewrite each expression as a single power of 2.

**a. \(4^{10}\):**
- \(4\) is \(2^2\), so:
  \[
  4^{10} = (2^2)^{10} = 2^{20}
  \]

**b. \(8^x \times 2^4\):**
- \(8\) is \(2^3\), so:
  \[
  8^x \times 2^4 = (2^3)^x \times 2^4 = 2^{3x} \times 2^4 = 2^{3x+4}
  \]

**c. \(16^{\frac{2}{3}}\):**
- \(16\) is \(2^4\), so:
  \[
  16^{\frac{2}{3}} = (2^4)^{\frac{2}{3}} = 2^{\frac{8}{3}}
  \]

**d. \(2^x \times 4^y \times 8^z \times 16\):**
- Rewrite \(4\), \(8\), and \(16\) in terms of powers of 2:
  \[
  2^x \times (2^2)^y \times (2^3)^z \times 2^4 = 2^x \times 2^{2y} \times 2^{3z} \times 2^4 = 2^{x+2y+3z+4}
  \]

**e. \(2\sqrt{2}\):**
- \(\sqrt{2} = 2^{1/2}\), so:
  \[
  2\sqrt{2} = 2^1 \times 2^{1/2} = 2^{1 + \frac{1}{2}} = 2^{\frac{3}{2}}
  \]

**f. \(\frac{4}{\sqrt{2}}\):**
- Rewrite \(4\) and \(\sqrt{2}\) as powers of 2:
  \[
  \frac{4}{\sqrt{2}} = \frac{2^2}{2^{1/2}} = 2^{2 - \frac{1}{2}} = 2^{\frac{3}{2}}
  \]

**g. \(4^{1/3} \times 8^{1/5}\):**
- Rewrite \(4\) and \(8\) as powers of 2:
  \[
  4^{1/3} \times 8^{1/5} = (2^2)^{1/3} \times (2^3)^{1/5} = 2^{\frac{2}{3}} \times 2^{\frac{3}{5}} = 2^{\frac{2}{3} + \frac{3}{5}} = 2^{\frac{19}{15}}
  \]

### Summary:
a. \(2^{20}\)  
b. \(2^{3x + 4}\)  
c. \(2^{\frac{8}{3}}\)  
d. \(2^{x + 2y + 3z + 4}\)  
e. \(2^{\frac{3}{2}}\)  
f. \(2^{\frac{3}{2}}\)  
g. \(2^{\frac{19}{15}}\)

Would you like more details on any step?

Here are five related questions:
1. How do you simplify expressions with fractional exponents?
2. What are the general properties of exponents?
3. How do you handle exponents when multiplying or dividing terms?
4. How would you express roots as fractional powers?
5. How do you combine terms with different bases and exponents?

**Tip:** Always express roots and radicals in terms of fractional exponents for easier simplification.

Write as a single power of 2:
a. 4^10
b. 8^x times 2^4
c. 16^2/3
d. 2^x times 4^y times 8^z times 16
e. 2√2
f. 4/√2
g. 4^1/3 times 8^1/5

Learn how to express exponential expressions such as 4^10, 8^x times 2^4, and more as a single power of 2. This problem covers exponentiation, properties of exponents, and radicals, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation