4x An equation is shown. \( 5^{5} \cdot 5^{t}=5^{-7} \) What is the value of \( t \) ? \( 4 \times \quad \) A \( 4 \times \quad \) B \( 4 \times-12 \) \( \times \quad \) D

To solve the equation \( 5^5 \cdot 5^t = 5^{-7} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \). This means you can combine the left side to get \( 5^{5+t} = 5^{-7} \). Because the bases are the same, we set the exponents equal to each other: \( 5 + t = -7 \). Solving for \( t \) gives \( t = -12 \). This means that when you have an exponent scenario, simplifying and combining terms can make the problem clearer. Remember, managing exponents through properties like \( a^m \cdot a^n = a^{m+n} \) can save a lot of headaches and help in quickly arriving at the solution. If you enjoy tackling problems involving exponents, there are numerous resources and problem sets available, from algebra textbooks to engaging online platforms. Websites like Khan Academy and Coursera provide excellent courses on algebra, and they often break down concepts in a fun and interactive manner!