Step-by-step explanation:
Our expression;
[tex]\frac{4^5\times4^7}{4^-2}[/tex]
Notes;
When exponents multiply, they add.
When exponents divide, they subtract.
Multiply;
[tex]\frac{4^5\times4^7}{4^{-2}}=\frac{4^{-2}}{4^{-2}}[/tex]
Divide;
[tex]\boxed{\frac{4^{-2}}{4^{-2}}=4^0=1}[/tex]
Facts to review:
[tex]\bullet \ \tex\text{Tip 1: If there is a "multiplication" sign, then the exponents will add.} \\\\ \bullet \ \tex\text{Tip 2: If there is a "division" sign, then the exponents will subtract.}\\\\ \bullet \ \ \tex\text{Tip 3: If a number, exponent, fraction, etc. is divided by itself, the result is 1.}[/tex]
Step- by step calculations:
[tex]\bullet\rightarrow (4^{5} \times 4^{-7} ) \div 4^{-2} \\\\ \bullet\rightarrow (4^{5 +(- 7)} ) \div 4^{-2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\tex\text{Tip 1}]\\\\ \bullet\rightarrow (4^{-2} ) \div 4^{-2}\\\\ \bullet\rightarrow \boxed{\bold{1}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\tex\text{Tip 3}][/tex]
The solution for the given expression is 1.
