Exponent Laws: Same Base or Same Exponent
Powers multiply by adding exponents, nest by multiplying them, and distribute over a product -- each law read straight off the meaning of a power as repeated multiplication. The problems here rewrite to a common base or a common exponent, or factor a shared power out of a sum, and then compare what is left; pairing 2s with 5s to make powers of ten is the same rewrite, and some use a given inequality to bound the result.
grade 8 Expressions Convert to AlgebraLook for a Pattern
Progression (7)
g8 1. Same exponent, so match the bases Expressions
g8 2. Match the exponents, then compare bases Expressions
g8 3. Rewrite in base 2 and factor the sum Expressions
g8 4. Pair 2s with 5s to make powers of ten Expressions
g8 5. Solve for the building blocks, then rebuild Expressions
g8 6. Multiply top and bottom to use the given power ExpressionsNumber system
g8 7. Chain the given inequality twice Expressions