Solve each one.
•10 to the power of 8 over 10 to the power of 8
•10 to the power of 8 over 10 to the power of 10
•10 to the power of 5 multiply 10 to the power of -4
• (10 to the power -2) to the power -2
• 10 to the power of 8 over 10 to the power of 8:
When we divide two numbers with the same base but different exponents, the exponents cancel out. Therefore, it simplifies to 10 to the power of 8 minus 8, which is equal to 10 to the power of 0. Any number raised to the power of 0 is equal to 1. So, the answer is 1.
• 10 to the power of 8 over 10 to the power of 10:
Similarly, when we divide two numbers with the same base but different exponents, the exponents cancel out. In this case, it simplifies to 10 to the power of 8 minus 10, which is equal to 10 to the power of -2. So, the answer is 10 to the power of -2.
• 10 to the power of 5 multiplied by 10 to the power of -4:
When we multiply two numbers with the same base, we add the exponents. In this case, it simplifies to 10 to the power of 5 plus -4, which is equal to 10 to the power of 1. So, the answer is 10 to the power of 1, which equals 10.
• (10 to the power of -2) to the power of -2:
When we raise a number to a power and then raise that result to another power, we multiply the exponents. In this case, it simplifies to 10 to the power of -2 multiplied by -2, which is equal to 10 to the power of -4. So, the answer is 10 to the power of -4.