Question

Which expressions are equivalent to 4 Superscript 13​?
StartFraction 4 Superscript 22 Over 4 Superscript 9 EndFraction
StartFraction 4 Superscript 7 Over 4 Superscript 6 EndFraction
4 Superscript 9 Baseline times 4 Superscript 4
4 Superscript 7 Baseline times 4 Superscript 6
Question content area bottom
Part 1
Select all that apply.
A.4 Superscript 9 Baseline times 4 Superscript 4
4 Superscript 9 Baseline times 4 Superscript 4
B.StartFraction 4 Superscript 7 Over 4 Superscript 6 EndFraction
StartFraction 4 Superscript 7 Over 4 Superscript 6 EndFraction
C.StartFraction 4 Superscript 22 Over 4 Superscript 9 EndFraction
StartFraction 4 Superscript 22 Over 4 Superscript 9 EndFraction
D.4 Superscript 7 Baseline times 4 Superscript 6
4 Superscript 7 Baseline times 4 Superscript 6

Answer 1

To determine which expressions are equivalent to \(4^{13}\), we can simplify each expression using the properties of exponents.

1. **Expression A: \(4^{9} \times 4^{4}\)**
Using the property of exponents that states \(a^m \times a^n = a^{m+n}\), we have:
\[
4^{9} \times 4^{4} = 4^{9+4} = 4^{13}
\]
This expression is equivalent to \(4^{13}\).

2. **Expression B: \(\frac{4^{7}}{4^{6}}\)**
Using the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\), we have:
\[
\frac{4^{7}}{4^{6}} = 4^{7-6} = 4^{1}
\]
This expression is not equivalent to \(4^{13}\).

3. **Expression C: \(\frac{4^{22}}{4^{9}}\)**
Using the same property of exponents, we have:
\[
\frac{4^{22}}{4^{9}} = 4^{22-9} = 4^{13}
\]
This expression is equivalent to \(4^{13}\).

4. **Expression D: \(4^{7} \times 4^{6}\)**
Again, using the property of exponents, we have:
\[
4^{7} \times 4^{6} = 4^{7+6} = 4^{13}
\]
This expression is equivalent to \(4^{13}\).

Now we can summarize the results:

- **A**: Equivalent to \(4^{13}\)
- **B**: Not equivalent to \(4^{13}\)
- **C**: Equivalent to \(4^{13}\)
- **D**: Equivalent to \(4^{13}\)

The expressions that are equivalent to \(4^{13}\) are **A, C, and D**.