Question

anne arundel county public schools | division of academics
7.3 whats in the cloud?
$2^{4}=2^{(3+?)}$
$3^{(2*?)}=3^{12}$
$5^{?}=5^{(3(1+6))}$
$4^{(2*8)}=?^{16}$
$3^{10}=3^{(?-12)}$
$2^{?}=2^{4}*2^{5}$
how did you determine the missing number for each cloud?
discuss your response with others. then summarize your findings.

Explanation:

Step1: Solve $2^4=2^{(3+?)}$

Set exponents equal: $4=3+x$
$x=4-3=1$

Step2: Solve $3^{(2*?)}=3^{12}$

Set exponents equal: $2x=12$
$x=\frac{12}{2}=6$

Step3: Solve $5^?=5^{(3(1+6))}$

Simplify right exponent: $3(7)=21$
Set exponents equal: $x=21$

Step4: Solve $4^{(2*8)}=?^{16}$

Simplify left exponent: $2*8=16$
Base matches: $x=4$

Step5: Solve $3^{10}=3^{(?-12)}$

Set exponents equal: $10=x-12$
$x=10+12=22$

Step6: Solve $2^?=2^4*2^5$

Add exponents: $4+5=9$
Set exponents equal: $x=9$

Answer:

1. $1$
2. $6$
3. $21$
4. $4$
5. $22$
6. $9$