Final answer:
Exponential form of 4⁶ ⋅ 4³ is 4⁹, 0.000078 in scientific notation is 7.8 × 10-5, and x⁴/x⁻² simplifies to x⁶.
Step-by-step explanation:
The exponential form of 4⁶ ⋅ 4³ can be found by using the rule of exponents which states that when we multiply two powers with the same base, we add the exponents. Hence, 4⁶ ⋅ 4³ = 4⁹.
To write 0.000078 in scientific notation, we move the decimal point five places to the right, giving us 7.8, and thus, the number is 7.8 × 10-5.
The expression x⁴/x⁻² is simplified by using the rule that when we divide two powers with the same base, we subtract the exponents. So x⁴/x⁻² simplifies to x⁶.